Final answer:
If two ideal gases A and B are at the same temperature, they would have proportional internal energies, and the ratios of their moles and atomic masses can be determined. They also exhibit ideal gas behavior when subject to low pressure and high temperature.
Step-by-step explanation:
If two ideal gases, A and B, are at the same temperature, several inferences can be made about their behavior based on the principles of kinetic molecular theory and the ideal gas law.
Firstly, the internal energy of an ideal gas is solely dependent on temperature. Given that gases A and B are at the same temperature, they would have proportional internal energies based on their respective amounts (in moles). An implication of this is seen where 1.0 g of gas A has the same internal energy as 0.10 g of gas B. This means that the ratio of the number of moles of each gas (a) and the ratio of the atomic masses of the two gases (b) can be determined from their respective masses and the fact that the internal energy per mole at a given temperature is the same for all ideal gases.
Another inference is based on Graham's Law of Effusion, which states that if two gases A and B are at the same temperature and pressure, the ratio of their effusion rates is inversely proportional to the ratio of the square roots of the masses of their particles. In this scenario, since the particles have the same kinetic energy due to the same temperature, heavier particles will move slower, and lighter particles will move faster.
Ideal gas behavior is a key assumption when discussing the behavior of gases A and B. It's important to note that ideal behavior is an approximation that holds true under conditions of relatively low pressure and high temperature. At these conditions, gases behave in a way that's closely aligned with the ideal gas law, where the variables of pressure (P), volume (V), and temperature (T) are connected in a simple relationship and effects due to intermolecular forces or the volume occupied by gas molecules themselves can be ignored.